Subtract rational expression. Show work please.

Question

asked Jul 21, 2021 192k views

1 Answer

Pjcabrera · Answer 1 · 2021-07-27T01:46:01+0000

Given:

$(x+4)/(x-1)-(5)/(x^(2)-1)

To find:

The simplified rational expression by subtraction.

Solution:

Let us factor
x^2-1 . It can be written as
x^2-1^2 .

x^2-1^2=(x-1)(x+1) using algebraic identity.

$(x+4)/(x-1)-(5)/(x^(2)-1)=(x+4)/(x-1)-(5)/((x+1)(x-1))

LCM of
x-1,(x+1)(x-1)=(x+1)(x-1)

Make the denominators same using LCM.

Multiply and divide the first term by (x + 1) to make the denominator same.

$=((x+4)(x+1))/((x-1)(x+1))-(5)/((x-1)(x+1))

Now, denominators are same, you can subtract the fractions.

$=((x+4)(x+1)-5)/((x-1)(x+1))

Expand
(x+4)(x+1)-5 .

$=(x^2+4x+x+4-5)/((x-1)(x+1))

$=(x^(2)+5 x-1)/((x-1)(x+1))

$(x+4)/(x-1)-(5)/(x^(2)-1)=(x^(2)+5 x-1)/((x-1)(x+1))